Organization
Faculty of Humanities and Social Sciences Professor
Position
Professor
External link
MURAI Joshin
Degree
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博士(理学) ( 大阪大学 )
Research Interests
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Econophysics
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Probability Theory
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経済物理学
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確率論
Research Areas
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Natural Science / Applied mathematics and statistics
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Social Infrastructure (Civil Engineering, Architecture, Disaster Prevention) / Safety engineering
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Social Infrastructure (Civil Engineering, Architecture, Disaster Prevention) / Social systems engineering
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Natural Science / Basic mathematics
Education
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Osaka University 理学研究科 数学
- 1997
Country： Japan
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Osaka University 理学部 数学科
- 1990
Country： Japan
Research History
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- Professor,Graduate School of Humanities and Social Sciences,Okayama University
2012
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- 岡山大学社会文化科学研究科 教授
2012
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Associate Professor,Graduate School of Humanities and Social Sciences,Okayama University
2004 - 2012
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岡山大学社会文化科学研究科 准教授
2004 - 2012
Professional Memberships
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進化経済学会
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日本数学会
Papers
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Multiplicative random cascades with additional stochastic process in financial markets Reviewed
Jun-ichi Maskawa, Koji Kuroda, Joshin Murai
Evolutionary and Institutional Economics Review 15 ( 2 ) 515 - 529 2018.12
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A model of transaction signs with order splitting and public information Reviewed
Joshin Murai
Evolutionary and Institutional Economics Review 13 ( 2 ) 469 - 480 2016.12
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公開情報と取引符号
村井浄信
The Institute of Statistical Mathematics Cooperative Research Report 360 116 - 125 2016
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公開情報への反応関数をもつポリマーモデルにおける大数の強法則
村井浄信
岡山大学経済学会雑誌 47 ( 2 ) 117 - 128 2016
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Signs of market orders and human dynamics Reviewed
Joshin Murai
Proceedings of the International Conference on Social Modeling and Simulation, plus Econophysics Colloquium 2014 39 - 50 2015
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取引間隔の多様なベキ指数と取引符号のハースト指数
村井浄信
The Institute of Statistical Mathematics Cooperative Research Report 332 97 - 102 2015
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Application of the Cluster Expansion to a Mathematical Model of the Long Memory Phenomenon in a Financial Market Reviewed
Koji Kuroda, Jun-ichi Maskawa, Joshin Murai
JOURNAL OF STATISTICAL PHYSICS 152 ( 4 ) 706 - 723 2013.8
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Market-wide price co-movement around crashes in Tokyo stock exchange Reviewed
J.Maskawa, J.Murai, K.Kuroda
Evolutionary and Institutional Economic Review 10 ( 1 ) 81 - 92 2013
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Long Memory in Trade Signs and Short Memory in Stock Prices Reviewed
Koji Kuroda, Jun-ichi Maskawa, Joshin Murai
PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT 194 ( 194 ) 11 - 27 2012
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Stock price process and long memory in trade signs Reviewed
Koji Kuroda, Jun-ichi Maskawa, Joshin Murai
ADVANCES IN MATHEMATICAL ECONOMICS, VOL 14 14 69 - + 2011
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株価変動過程と売買符号のLong Memory
黒田耕嗣, 増川純一, 村井浄信
物性研究 93 ( 5 ) 633 - 636 2010
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Stock price process and long memory in trade sign
K.Kuroda, J.Murai
統計数理研究所共同研究リポート 247 59 - 76 2009
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Graphs for Menshikov-Zuev's Problems on ρ-percolation model
J.Murai
岡山大学経済学会雑誌 40 ( 4 ) 115 - 125 2009
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Long Memory in Finance and Fractional Brownian Motion Reviewed
Koji Kuroda, Joshin Murai
PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT ( 179 ) 26 - 37 2009
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符号相関についての数学モデル
黒田耕嗣, 村井浄信
The Institute of Statistical Mathematics Cooperative Research Report 209, Econophysics and its Applications ( 4 ) 87 - 95 2008
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Fat tail phenomena in a stochastic model of stock market : the long-range percolation approach
Kuroda Koji
39 ( 4 ) 151 - 176 2008
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A probabilistic model on the long memory property in stock market
K.Kuroda, J.Murai
Internaional conference 2008 in Okayama, Rising Economies and Regional Cooperation in the East Asia and Europe 1 - 20 2008
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Limit theorems in financial market models Reviewed
Koji Kuroda, Joshin Murai
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 383 ( 1 ) 28 - 34 2007.9
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Wulff shape and stock price process
K.Kuroda, J.Murai
Econophysics and its applications (2), The institute of statistical mathematics cooperative research report 2006
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Application of statistical mechanics to stock price processes
黒田耕嗣, 村井浄信
Proceedings of the First Sapporo Workshop on Financial Engineering and Its Applications 2005
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The Dobrushin-Hryniv theory for the two-dimensional latttice Widom-Rowlinson model Reviewed
Y. Higuchi, J. Murai, J. Wang
Adv. Stud. Pure Math. 2004
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Fluctuations of shapes for small area conditions
樋口保成, 村井浄信, 王軍
日本数学会２００３年度秋季総合分科会統計数学分科会予稿集 2003
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相分離クラスタの確率過程
村井浄信
電子情報通信学会誌 2002
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Critical probabilities on r-percolation model
村井浄信
平成１０年度〜平成１２年度科学研究費補助金（基盤研究(B)(2)）研究成果報告書『フラクタル上の解析学の展開』（課題番号10440029） 2001
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The central limit theorem of the Dobrushin-Hryniv type for the phase separation line of the Widom-Rowlinson model
Y. Higuchi, J. Wang, Joushin Murai
科研費シンポジウム「流体力学極限とその周辺」予稿集 2001
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Glauber-type dynamicsのシミュレーションについて
村井浄信
平成９年度〜平成１１年度科学研究費補助金（基盤研究(B)(2)）研究成果報告書『ランダム系の臨界現象の解析』（課題番号09440079） 2000
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密度付きパーコレーションモデルにおける臨界確率の評価について
村井浄信
平成９年度〜平成１１年度科学研究費補助金（基盤研究(B)(2)）研究成果報告書『ランダム系の臨界現象の解析』（課題番号09440079） 2000
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A gap between the rho-percolation threshold and percolation threshold.
Joushin MURAI
科研費研究集会「臨界現象の確率モデルとその周辺」予稿集 1998
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Percolation in high dimensional menger sponges Reviewed
Joushin Murai
Kobe journal of mathematics 14 ( 1 ) 49 - 61 1997
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Diffusion processes on Mandala Reviewed
J Murai
OSAKA JOURNAL OF MATHEMATICS 32 ( 4 ) 887 - 917 1995.12
Books
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株式市場のマルチフラクタル解析
黒田, 耕嗣, 増川, 純一, 村井, 浄信
日本評論社 2021.4 （ ISBN:9784535789050 ）
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株価の経済物理学
培風館 2011
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Econophysics and stock price
BAIFUKAN CO., LTD 2011
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ファイナンス・保険数理の現代的課題
日本大学文理学部 2008
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フラクタル幾何学
共立出版 2006
MISC
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Stock price process and the long-range percolation Reviewed
K.Kuroda, J.Murai
Practical Fruits of Econophysics 2005
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Stock price process and the long-range percolation.
黒田耕嗣, 村井浄信
数理解析研究所講究録 2004
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Stock price process and the long-range percolation
黒田耕嗣, 村井浄信
共同研究集会「経済の数理解析」予稿集 2003
Presentations
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注文分割と公開情報による取引符号モデル
経済物理とその周辺 2016
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公開情報と取引符号
経済物理とその周辺 2015
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公開情報への反応関数をもつポリマーモデルにおけるトレンド項
無限粒子系、確率場の諸問題XI 2015
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注文分割と公開情報による取引符号モデル
経済物理学 2015: 新たな方向性を求めて 2015
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Order signs model with order splitting and exogenous herding
International Conference on Big data in Economics, Science and Technology 2015
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A model of order signs under multiple order splitting and public information
ECONOPHYS-2015 2015
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Signs of market orders and human dynamics
経済物理学とその周辺 2014
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Signs of market orders and human dynamics
Social Modeling and Simulations + Econophysics Colloquium 2014 2014
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無限分割ポリマーモデルのスケール極限
Okayama Analysis and Probability Seminar 2014
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Application of the cluster expansion to a mathematical model of the long memory phenomenon in a financial market
新潟確率論ワークショップ 2013
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Application of the cluster expansion to a mathematical model of the long memory phenomenon in a financial market
2013
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Application of the cluster expansion for financial market
無限粒子系、確率場の諸問題VII 2011
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金融市場における余震の数理モデル
経済物理とその周辺 2011
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FinanceにおけるLong Memory Process
無限粒子系、確率場の諸問題VI 2011
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A probabilistic model on the long memory property in stock market
Rising Economies and Regional Cooperation in the East Asia and Europe 2008
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Long Memory in Finance
無限粒子系、確率場の諸問題III 2008
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符号相関についての数学モデル
平成１９年度統数研研究会「経済物理とその周辺」第１回研究会 2007
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Limit theorems in financial market models
Econophysics Colloquium 2006 2006
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株価変動過程への統計力学的アプローチ
平成１７年度統数研研究会「経済物理とその周辺」第２回研究会 2006
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株式市場モデルへのDobrushin-Hryniv理論の応用
平成１７年度統数研研究会「経済物理とその周辺」第１回研究会 2005
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Application of statistical mechanics to stock price processes
金融工学２００４科研費研究集会 2005
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Stock price process and the long-range percolation
第３回日経エコノフィジックス・シンポジウム 2004
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Toward the Dobrushin-Hryniv theorem for a Pirogov-Sinai type symmetric model
Infinite Particle Systems and Critical Phenomena 2004
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Stock price process and the long-range percolation
共同研究集会「経済の数理解析」 2003
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Stock price process and the long-range percolation
科研費シンポジウム「パーコレーション，無限粒子系とその周辺」 2003
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Fluctuations of shapes for small area conditions
日本数学会２００３年度秋季総合分科会統計数学分科会 2003
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The central limit theorem of the Dobrushin-Hryniv type for the phase separation line of the Widom-Rowlinson model
科研費シンポジウム「流体力学極限とその周辺」 2001
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The central limit theorem of the Dobrushin-Hryniv type for the phase separation line of the Widom-Rowlinson model.
科研費シンポジウム「流体力学極限とその周辺」 2001
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The central limit theorem of the Dobrushin-Hryniv type for the phase separation line of the Widom-Rowlinson model.
流体力学極限とその周辺 2001
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２次元Widom-Rowlinsonモデルの相分離クラスターの中心極限定理
日本数学会２００１年度秋季総合分科会統計数学分科会 2001
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ρパーコレーションにおける臨界確率について
九州大学確率論セミナー 1999
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\rho-percolation
大阪大学高橋研究室セミナー 1999
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\rho-percolation
高橋研究室セミナー 1999
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Critical probabilities on r-percolation model
共同研究集会、「フラクタル上の解析学と幾何学の相互作用」 1999
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Critical probabilities on r-percolation model.
フラクタル上の解析学と幾何学の相互作用 1999
Research Projects
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自己励起型ポリマーモデルによる株式市場の時間相関の研究
Grant number：18K04612 2018.04 - 2023.03
日本学術振興会 科学研究費助成事業 基盤研究(C)
村井 浄信
Grant amount：\4160000 （ Direct expense: \3200000 、 Indirect expense：\960000 ）
株式市場では，秒単位あるいはそれ以下の極めて短いタイムスパンで取引が行われている。それら全てを記録した高頻度な取引データの解析から，次々と新たな知見が得られている。従来の日次データ（日毎の４本値データ）の解析を通して見えていた市場の姿とは大きく異なる，本来の市場の姿と呼ぶべきものが，このビッグ・データ解析を通して観察できるようになった。本研究は，市場のその新たな姿を理論的に理解することを試みるものである。ミクロな個々の市場参加者は違いに影響を与え合いながら投資行動を行い，それらが集積することによって，マクロな市場の動きが形作られていく。ここでは，ミクロな相互作用の集積を上手に取り扱うことができる統計力学の手法を用いて，理論モデルを構築する。具体的には，個々の市場参加者の投資行動を離散時間をベースとするポリマーで表現し，ポリマーの集まりによって，離散時間の確率過程を定義する。そして，統計力学のクラスター展開の手法を用いることで，連続時間の確率過程を構築し，それが実際に市場で観察されている現象を再現することを確かめる。本年度は株式市場における対数収益率の時系列データが持つマルチフラクタル性をタイムスケールの異なる市場参加者間の相互作用で説明を試みる理論研究について，この数年間の研究を整理する作業を行った。その成果を『株式市場のマルチフラクタル解析』という本（共著）にまとめ，２０２１年に刊行した。
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Statistical mechanical study of stochastic models for time correlation in stock markets
Grant number：15K01190 2015.04 - 2019.03
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Murai Joshin, Kuroda Koji, Maskawa Jun-ichi
Grant amount：\4160000 （ Direct expense: \3200000 、 Indirect expense：\960000 ）
By analyzing huge high frequency data in stock market, phenomena that can not be observed in daily data are discovered one after another. In this study, we have theoretically studied the causes of long-term memory of the transaction signs among those phenomena, using statistical mechanics methods. Based on the hypothesis that the origin is in the divided orders of potential orders by individual investors, we define a discrete time stochastic process that represents the cumulative transaction signs, and use the method of the cluster expansion of statistical mechanics to obtain a continuous time stochastic processes as its scale limit. It is shown that the time stochastic process is the superposition of Brownian motion and multiple fractional Brownian motions with different Hurst exponents.
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Empirical study and construction of stochastic processes on the long memory property of the time series of trade signs in a stock market.
Grant number：21510146 2009.04 - 2014.03
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
MURAI Joshin
Grant amount：\3900000 （ Direct expense: \3000000 、 Indirect expense：\900000 ）
We study the influence of the trader's investment strategy on the long memory property of the time series of trade signs in a stock market, using the stochastic process. We present a discrete time stochastic process for polymer model which describes trader's trading strategy to split his or her order into small pieces, and prove that its scaled process converges to superposition of multiple fractional Brownian motions with different Hurst exponents and a standard Brownian motion. We also show that their Hurst exponents are derived from the distribution of the time interval of split orders.
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Study of asymptotic theory for representations of symmetric groups from the viewpoint of scaling limits for probability models
Grant number：16540154 2004 - 2006
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
HORA Akihito, YAMADA Hiro-Fumi, MURAI Joshin, SASAKI Toru
Grant amount：\3600000 （ Direct expense: \3600000 ）
The main purpose of the present research is to study asymptotic behavior of various characteristic quantities of representations of symmetric groups and other similar discrete groups as the sizes of the groups grow, and to investigate the limiting pictures from the viewpoint of scaling limits in probability theory and statistical mechanics. Features to be noted in this research include using methods of limit theorems in quantum probability and making much of relations to free probability and random matrices. The following are several concrete results.
1. We studied the spectral distributions of Laplacians with respect to the Gibbs states in zero temperature and infinite volume limit as graphs grow with their degrees and temperatures keeping certain scaling balances. We computed the asymptotic behavior in details under the formulation of quantum central limit theorem by using creation and annihilation operators on interacting Fock spaces.
2. Through combinatorial hard analysis of moments of the Jucys-Murphy element, we studied universal understanding of concentration phenomena in various statistical ensembles consisting of Young diagrams, including those which come from irreducible decomposition of a representation of the symmetric group such as the Littlewood-Richardson coefficients. Many of them are closely related to some properties of random walks on a certain modified Young graph. Here also we applied methods of quantum probability effectively.
3. Under cooperation with T. Hirai and E. Hirai, we constructed a nice factor representation which expresses any character of a wreath product of a compact group with the infinite symmetric group as its matrix element. This representation reflects directly the characterizing parameters for the character beyond a general representation of Gelfand-Raikov. -
Research of fluctuations of phase boundaries in large interacting systems from the probabilistic point of view
Grant number：15340032 2003 - 2006
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
HIGUCHI Yasunari, FUKUYAMA Katusi, ADACHI Tadayoshi, WATANABE Kiyoshi, YOSHIDA Nobuo, MURAI Joshin
Grant amount：\15300000 （ Direct expense: \15300000 ）
The main aim of this research is to understand the fluctuation of phase boundaries appearing in many mathematical models of phase transitions from the probabilistic view point. Essentially, we could do it only for the Widom-Rowlinson model in two dimensions as a conditional central limit theorem for phase boundaries. However, this type of phenomenon is now well understood during these four years by the works of Ioffe, Bodineau and others. There still remains to be understood related to this problem but we understand that the main problem is solved.
Our second aim was to understand the transition mechanism in percolation when the underlying graph has no translations which act as group of automorphisms of the underlying graph. A typical problem is in the case where the graph has infinitely ramified fractal structure. As an example, percolation in the Sierpinski carpet lattice has not been understood well. We could prove that percolation is sharp for this model. This has been open since 1997. The sharpness of the percolation transition is understood as
1.there is only one critical point
2.below the critical point, the connectivity function decays exponentially
3. above the critical point, the infinite cluster is unique and the dual connectivity decays exponentially with respect to the dual graph distance. -
Harmonic analysis on graphs and discrete groups, and scaling limit for probability models
Grant number：13640175 2001 - 2003
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
HORA Akihito, MURAI Joshin, SASAKI Toru
Grant amount：\3500000 （ Direct expense: \3500000 ）
The aim of this project is to read out statistical properties of huge systems characterized by a certain symmetry from the viewpoint of asymptotic spectral analysis and scaling limits by using the methods of harmonic analysis and representation theory. We obtained concrete results as follows.
1. We computed scaling limits for the spectral distributions of adjacency operators on graphs in the framework of quantum central limit theorem. We introduced Gibbs states as well as vacuum states on distance-regular graphs and investigated the limit picture in low temperature and high degrees especially for Johnson graphs. The result is described in terms of the interacting Fock space associated with Meixner polynomials. Interesting distributions are derived in the limit by using combinatorial structure of creators and annihilators.
2. We established a general theory for spectral analysis of graphs by the method of quantum decomposition. We revealed a connection of asymptotic characteristic values of regular graphs with the parameters of interacting Fock spaces. The limit distributions are systematically described by using methods of orthogonal polynomials and Green functions beyond computation of individual spectral limits. The item here is closely related to a joint work with Nobuaki Obata at Tohoku University.
3. We obtained an extension (a quantization) of Kerov's central limit theorem for irreducible characters and the Plancherel measure as an asymptotic aspect of representations of the symmetric groups. Since the result goes out of the framework of interacting Fock spaces, we introduced a modification of the usual Young graph as well as creators and annihilators on it. -
Research on the formation and fluctuation of random shapes in mathematical models of statistical mechanics
Grant number：12440027 2000 - 2002
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
HIGUCHI Yasunari, NAKANISHI Yasutaka, MIYAKAWA Tetsuro, FUKUYAMA Katsushi, MURAI Joushin, YAMAZAKI Tadashi
Grant amount：\10100000 （ Direct expense: \10100000 ）
1. We found a new proof of the fact that there are only two extremal Gibbs states for the two dimensional Ising model based on the percolation argument. As an application of this new method, we proved that there are only two extremal points of translationally invariant Gibbs states for the two dimensional Widom-Rowlinson model for sufficiently low temperatures.
2. We gave an estimate of the speed of convergence for the time constant of the first passage Ising percolation for temperatures above the critical point.
3. We proved a Dobrushin-Hryniv type limit theorem for the two-dimensional Widom-Rowlinson model. The conditions for the result to hold are a little relaxed. -
Harmonic analysis on discrete structures and its applications to classical and quantum probability models
Grant number：11640168 1999 - 2000
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
HORA Akihito, MURAI Joshin, SASAKI Toru, HIROKAWA Masao
Grant amount：\2900000 （ Direct expense: \2900000 ）
We studied asymptotic behavior of probability models by using the methods of harmonic analysis. Main results are included in 1. the cut-off phenomenon in random walks and 2. central limit theorems in algebraic probability.
1. The cut-off phenomenon is a sort of critical phenomenon widely observed in the process of convergence to the equilibrium for Markov chains. It is known that the multiplicities of eigenvalues of a transition matrix, which are caused by symmetry of the system, play an important role. In this project, we seeked a rigorous and practical criterion for the cut-off phenomenon beyond verification in individual models and intuitive understanding based on the degeneration of the second eigenvalue. Focusing on distance-regular graphs, we obtained a criterion described in terms of spectral data of the graph. This enables us to find models of the cut-off phenomenon systematically.
2. Quantum central limit theorems form a main stream in algebraic probability. In this project, we studied important relations between independence of noncommutative random variables and central limit theorems, making much of their algebraic and combinatorial aspects. As a concrete result, we mention the asymptotic spectral distribution of the Laplacian operator on a Johnson graph with respect to the Gibbs state under a low temperature and infinite volume limit. This result leads us to the consideration of creators and annihilators on a nontrivial interacting Fock space and hence gives a good working example in this direction. -
スピングラスの確立論的研究
Grant number：10874017 1998 - 1999
日本学術振興会 科学研究費助成事業 萌芽的研究
日野 正訓, 南 和彦, 吉田 伸生, 熊谷 隆, 村井 浄信
Grant amount：\2000000 （ Direct expense: \2000000 ）
本年度もセミナーや研究会を通じて、スピン系等の数理モデルの性質を中心に最新のプレプリントの紹介、各自の研究の報告・議論を行ったが、スピングラスのモデル自体について大きな進展を得ることは残念ながら出来なかった。以下では、セミナー等で得られた、このテーマに関連した問題に関する実績概要を述べる。
1.吉田は、wetting tansitionの問題に興味を持ち、E.BolthausenやP.Caputoらのプレプリントを読むとともに具体的な計算を行った。Wetting transitionの問題とは、固形物の上に液体がありpinningとentropy repulsionという対立する力がかかるとき、そのinterfaceの局在(dry phase)・非局在(wet phase)がどのようなときに起こるかという問題である。吉田は、非負に条件付けられた一次元のランダムウォークにpinningとしてdiluted local timeを与えたとき、pinningの係数が小さければ非局在、大きければ局在が起こることを示した。
2.熊谷は、フラクタルのような複雑な形の不純物が空間内に存在するときに、空間からこの物質内への熱伝導はどのようになるかという問題を扱い、実解析で用いられるBesov空間の理論を援用することによりある条件のもとでこのような熱伝導を表す拡散過程(物質内ではその物質の拡散をし、外では空間の拡散に従うようなもの)が構成できることを示した。この結果は、最近雑誌に掲載された。
3.村井は篠田氏(奈良女)との議論を通じて、ある範疇の自己相似なグラフ上ではρ-パーコレーションのρ→1における相転移点と普通のパーコレーションの相転移点が一致することを示し、現在論文を執筆中である。
Class subject in charge
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Graduation Research Seminar （2024academic year） 1st and 2nd semester - その他7～8
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Graduation Research Seminar （2024academic year） 3rd and 4th semester - その他7～8
-
Seminar （2024academic year） 1st and 2nd semester - 木7～8
-
Seminar （2024academic year） 3rd and 4th semester - 木7～8
-
Basic Seminar （2024academic year） Third semester - 火7～8
-
Applied Probability Model （2024academic year） special - その他
-
Seminar on Applied Probability Model 1 （2024academic year） special - その他
-
Seminar on Applied Probability Model 2 （2024academic year） special - その他
-
Probability Model （2024academic year） Prophase - 木2
-
Seminar on Probability Model （2024academic year） Late - 木2
-
Seminar on Probability Model 1 （2024academic year） Prophase - 木2
-
Seminar on Probability Model 2 （2024academic year） Late - 木2
-
Economic and Business Mathematics （2024academic year） 1st and 2nd semester - 金10
-
Economic and Business Mathematics I （2024academic year） 3rd and 4th semester - 金5～6
-
Economic and Business Mathematics II （2024academic year） 3rd and 4th semester - 金5～6
-
Graduation Research Seminar （2023academic year） 1st and 2nd semester - その他7～8
-
Graduation Research Seminar （2023academic year） 3rd and 4th semester - その他7～8
-
Seminar （2023academic year） 1st and 2nd semester - 木7～8
-
Seminar （2023academic year） 3rd and 4th semester - 木7～8
-
Basic Seminar （2023academic year） Third semester - 火7～8
-
Applied Probability Model （2023academic year） Prophase - その他
-
Seminar on Applied Probability Model 1 （2023academic year） special - その他
-
Seminar on Applied Probability Model 2 （2023academic year） special - その他
-
Probability Model （2023academic year） Prophase - 木2
-
Seminar on Probability Model （2023academic year） Late - 木2
-
Seminar on Probability Model 1 （2023academic year） Prophase - 木2
-
Seminar on Probability Model 2 （2023academic year） Late - 木2
-
Economic and Business Mathematics （2023academic year） 1st and 2nd semester - 水10
-
Economic and Business Mathematics I （2023academic year） 1st and 2nd semester - 金5～6
-
Economic and Business Mathematics II （2023academic year） 3rd and 4th semester - 金5～6
-
Graduation Research Seminar （2022academic year） 1st and 2nd semester - その他
-
Graduation Research Seminar （2022academic year） 3rd and 4th semester - その他
-
Seminar （2022academic year） 1st and 2nd semester - 木7～8
-
Seminar （2022academic year） 3rd and 4th semester - 木7～8
-
Basic Seminar （2022academic year） Third semester - 火7～8
-
Applied Probability Model （2022academic year） special - その他
-
Seminar on Applied Probability Model 1 （2022academic year） special - その他
-
Seminar on Applied Probability Model 2 （2022academic year） special - その他
-
Probability Model （2022academic year） Prophase - 木2
-
Seminar on Probability Model （2022academic year） Late - 木
-
Seminar on Probability Model 1 （2022academic year） Prophase - 木2
-
Seminar on Probability Model 2 （2022academic year） Late - 木2
-
Economic and Business Mathematics （2022academic year） 1st and 2nd semester - 水10
-
Economic and Business Mathematics I （2022academic year） 1st and 2nd semester - 金5～6
-
Economic and Business Mathematics II （2022academic year） 3rd and 4th semester - 金5～6
-
Challenge Seminar 1(Division of Economic Theory and Policy) （2022academic year） Prophase - その他
-
Challenge Seminar 2(Division of Economic Theory and Policy) （2022academic year） Late - その他
-
Graduation Research Seminar （2021academic year） 1st and 2nd semester - その他
-
Graduation Research Seminar （2021academic year） 3rd and 4th semester - その他
-
Seminar （2021academic year） 1st and 2nd semester - 木7～8
-
Seminar （2021academic year） 3rd and 4th semester - 木7～8
-
Seminar （2021academic year） 3rd and 4th semester - 木7～8
-
Basic Seminar （2021academic year） Third semester - 火7～8
-
Applied Probability Model （2021academic year） special - その他
-
Seminar on Applied Probability Model 1 （2021academic year） special - その他
-
Seminar on Applied Probability Model 2 （2021academic year） special - その他
-
Probability Model 1 （2021academic year） Prophase - 木2
-
Probability Model 2 （2021academic year） Late - 木2
-
Economic and Business Mathematics （2021academic year） 1st and 2nd semester - 金10
-
Economic and Business Mathematics （2021academic year） 1st and 2nd semester - 金10
-
Economic and Business Mathematics I （2021academic year） 1st and 2nd semester - 金5～6
-
Economic and Business Mathematics I （2021academic year） 1st and 2nd semester - 金5～6
-
Economic and Business Mathematics II （2021academic year） 3rd and 4th semester - 金5～6
-
Economic and Business Mathematics II （2021academic year） 3rd and 4th semester - 金5～6
-
Graduation Research Seminar （2020academic year） 1st and 2nd semester - その他
-
Graduation Research Seminar （2020academic year） 3rd and 4th semester - その他
-
Seminar （2020academic year） 1st and 2nd semester - 火7,火8
-
Seminar （2020academic year） 3rd and 4th semester - 木7,木8
-
Graduation Thesis （2020academic year） 1st-4th semester - その他
-
Basic Seminar （2020academic year） 1st semester - 木7,木8
-
Basic Seminar （2020academic year） Third semester - 火7,火8
-
Basic Seminar （2020academic year） Fourth semester - 火7,火8
-
Applied Probability Model （2020academic year） special - その他
-
Seminar on Applied Probability Model 1 （2020academic year） special - その他
-
Seminar on Applied Probability Model 2 （2020academic year） special - その他
-
Seminar on Probability Model 1 （2020academic year） Prophase - 木2
-
Seminar on Probability Model 2 （2020academic year） Late - 木2
-
Economic and Business Mathematics （2020academic year） 1st and 2nd semester - 木10
-
Economic and Business Mathematics II （2020academic year） Second semester - 金5,金6
-
Economic and Business Mathematics I （2020academic year） 1st semester - 金5,金6